H∞ Control with Output Weights For Descriptor Systems: An LMI Approach

This paper deals with a nonstandard H-infinity control problem for continuous-time descriptor systems with unstable and nonproper output weighting functions. In this problem, a desired controller is sought to render the closed-loop system comprehensively admissible and achieve some prescribed H-infinity performance for the closed-loop system as well. By a generalized Sylvester equation, the comprehensive admissibility objective is achieved using a specific structured controller. Thanks to this structured controller, the defined nonstandard control problem can be reduced to a standard H-infinity control problem for an associated descriptor plant. A numerically tractable solution is then derived in terms of a set of linear matrix inequalities (LMIs).